1. Field of the Invention
The present invention relates to a method of measuring strain with a strain gage.
2. Description of the Related Art
Generally, it has been known to measure a deformation of an object with a bridge, specifically, a Wheat-stone bridge, comprising a strain gage, as an arm, applied to the object for producing a resistance change depending on the strain and a plurality of resistors as other three arms.
Since strain of an object is proportional to stress to which the object is subjected, the term "strain" used herein will cover stress as well as strain in its original sense, and strain in its original sense will be denoted by the reference character ".epsilon." with or without any subscripts.
Methods of measuring strain with a bridge which has a strain gage, as one arm, applied to an object whose strain is to be measured are classified into one-gage methods and two-gage common-dummy methods. The one-gage methods include a one-gage two-wire method and a one-gage three-wire method.
FIG. 1 of the accompanying drawings shows a circuit illustrative of the one-gage two-wire method which is the most basic method of measuring strain with a bridge. According to the one-gage two-wire method, as shown in FIG. 1, two leads 2, 3 are connected to respective opposite terminals of a strain gage 1 applied to an object whose strain is to be measured. The method is called a two-wire method because of the two leads 2, 3 connected to the strain gage 1. The strain gage 1 is connected by the leads 2, 3 to a resistive circuit composed of resistors 4, 5, 6. The strain gage 1 and the resistors 4, 5, 6 jointly make up a bridge 7 which has the strain gage 1 (specifically, the strain gage 1 and the leads 2, 3) as one arm and the resistors 4, 5, 6 as other three arms.
The resistors 4, 5, 6 basically comprise resistive elements whose respective resistances R.sub.2, R.sub.3, R.sub.4 are constant irrespective of strain developed in the object, e.g., resistive elements having respective fixed resistances. Usually, the resistances R.sub.2, R.sub.3, R.sub.4 of the resistors 4, 5, 6 are represented by R.sub.0 =R.sub.2 =R.sub.3 =R.sub.4 where R.sub.0 is the reference resistance of the strain gage 1 when no strain is developed by the strain gage 1, i.e., the nominal resistance of the strain gage 1.
For measuring strain of the object with the bridge 7, a power supply voltage V (constant voltage) from a power supply for the bridge 7 is applied between power corners I.sub.1, I.sub.2 (at diagonally opposite junctions of the bridge 7). The power corner I.sub.1 is located at the junction between the lead 2 and the resistor 6 or a point at the same potential as the junction between the lead 2 and the resistor 6, and the power corner I.sub.2 is located at the junction between the resistor 4 and the resistor 5 or a point at the same potential as the junction between the resistor 4 and the resistor 5. With the power supply voltage V being applied between the power corners I.sub.1, I.sub.2, an output voltage e of the bridge 7 is detected between signal corners O.sub.1, O.sub.2 (at other diagonally opposite junctions of the bridge 7). The signal corner O.sub.1 is located at the junction between the lead 3 and the resistor 4 or a point at the same potential as the junction between the lead 3 and the resistor 4, and the signal corner O.sub.2 is located at the junction between the resistor 5 and the resistor 6 or a point at the same potential as the junction between the resistor 5 and the resistor 6.
If it is assumed that the leads 2, 3 have negligibly small resistances r.sub.a1, r.sub.a2 (r.sub.a1 .apprxeq.0, r.sub.a2 .apprxeq.0), and R.sub.0 =R.sub.2 =R.sub.3 =R.sub.4 as described above, then strain .epsilon. (in its original sense) developed in the object to which the strain gage 1 is applied and the output voltage e of the bridge 7 are related to each other according to the following equation (8): ##EQU1## where K represents the gage factor of the strain gage 1.
Therefore, by detecting the output voltage e of the bridge 7, the strain e of the object can be calculated from the detected output voltage e according to the equation (8).
For strain measurement, it is the general practice to set the power supply voltage V for the bridge 7 to V=2 (V) and to employ the strain gage 1 whose gage factor K is K=2. According to this general practice, the equation (8) is rewritten as follows: ##EQU2##
If the strain .epsilon. is sufficiently small (e&lt;&lt;1), then the denominator of the right-hand side of the equation (9) may be ignored, and the strain .epsilon. may be determined as .epsilon.=e. Furthermore, since the strain .epsilon. of the object and the stress .sigma. under which the object is placed to cause the strain .epsilon. are related to each other according to .sigma.=E.multidot..epsilon. (E represents the Young's modulus of the object), the stress to which the object is subjected can be determined from the output voltage e by multiplying the right-hand side of the equation (8) or (9) by the Young's modulus E of the object.
The above process is the basic process of measuring stress with a strain gage.
FIG. 2 of the accompanying drawings shows a circuit illustrative of the one-gage three-wire method. According to the one-gage three-wire method, as shown in FIG. 2, two leads 2, 3 are connected to respective opposite terminals of a strain gage 1 applied to an object whose strain is to be measured, and an auxiliary lead 8 is also connected to one of the terminals of the strain gage 1, i.e., the terminal thereof to which the lead 3 is connected. The method is called a three-wire method because of the three leads 2, 3, 8 connected to the strain gage 1.
As with the circuit for carrying out the one-gage two-wire method shown in FIG. 1, the strain gage 1 is connected by the leads 2, 3 to a resistive circuit composed of resistors 4, 5, 6, making up a bridge 9.
For measuring strain of the object with the bridge 9, a power supply voltage V (constant voltage) for the bridge 9 is applied between power corners I.sub.1, I.sub.2 (at diagonally opposite junctions of the bridge 9). The power corner I.sub.1 is located at the junction between the lead 2 and the resistor 6 or a point at the same potential as the junction between the lead 2 and the resistor 6, and the power corner 12 is located at the junction between the resistor 4 and the resistor 5 or a point at the same potential as the junction between the resistor 4 and the resistor 5.
According to the one-gage three-wire method, other diagonally opposite junctions of the bridge 9 are the terminal of the bridge 9 to which the leads 3, 8 are connected and the junction between the resistor 5 and the resistor 6 or a point at the same potential as the junction between the resistor 5 and the resistor 6. With the power supply voltage V being applied between the power corners I.sub.1, I.sub.2, an output voltage e of the bridge 9 is detected between signal corners O.sub.1, O.sub.2 at these other diagonally opposite junctions of the bridge 7. The auxiliary lead 8 is used to detect the output voltage e of the bridge 9. The arm of the bridge 9 which includes the strain gage 1 is made up of the strain gage 1 and the lead 2, and the arm of the bridge 9 which includes the resistor 4 is made up of the resistor 4 and the lead 3.
If it is also assumed, according to the one-gage three-wire method, that the leads 2, 3 have negligibly small resistances r.sub.a1, r.sub.a2 (r.sub.a1 .apprxeq.0, r.sub.a2 .apprxeq.0), and R.sub.0 =R.sub.2 =R.sub.3 =R.sub.4 as described above, then the above equation (8) is satisfied. If V=2 (V) and K=2, then the above equation (9) is satisfied. Therefore, strain .epsilon. developed in the object and stress to which the object is subjected can be calculated according to the equation (8) or (9). It is known that the one-gage three-wire method is more effective than the one-gage two-wire method to cancel the effect of a change in the resistances of the resistors 2, 3 due to a change in the ambient temperature on the strain measurement.
FIG. 3 of the accompanying drawings shows a circuit illustrative of a two-gage common-dummy method. According to the two-gage common-dummy method, as shown in FIG. 3, the circuit differs from the circuit according to the one-gage two-wire method shown in FIG. 2 in that the resistor 4 in the circuit shown in FIG. 2 is replaced with a strain gage 10 (called a dummy gage) as a resistor having the same characteristics as the strain gage 1. The strain gage 10 is incorporated in the arm with leads 11, 12 connected to respective terminals thereof. The strain gages 1, 10 and the resistors 5, 6 jointly make up a bridge 13.
The dummy gage 10 is positioned near the strain gage 1 applied to the object, i.e., in an area having the temperature environment as the strain gage 1 and free of strain. Since the dummy gage 10 has the same characteristics as the strain gage 1 and is positioned so as to be free of strain, the dummy gage 10 has a resistance R.sub.d which is basically equal to the reference resistance R.sub.0 of the strain gage 1 (R.sub.d =R.sub.0) According to the two-gage common-dummy method, it is also assumed that the resistances R.sub.3, R.sub.4 of the resistors 5, 6 are represented by R.sub.0 =R.sub.3 =R.sub.4.
For measuring strain of the object with the bridge 13, a power supply voltage V for the bridge 13 is applied between power corners I.sub.1, I.sub.2 (at diagonally opposite junctions of the bridge 13). The power corner I.sub.1 is located at the junction between the lead 2 and the resistor 6 or a point at the same potential as the junction between the lead 2 and the resistor 6, and the power corner I.sub.2 is located at the junction between the lead 12 and the resistor 5 or a point at the same potential as the junction between the lead 12 and the resistor 5. With the power supply voltage V being applied between the power corners I.sub.1, I.sub.2, an output voltage e of the bridge 13 is detected between signal corners O.sub.1, O.sub.2 (at other diagonally opposite junctions of the bridge 13). The signal corner O.sub.1 is located the junction between the lead 3 and the lead 11 or a point at the same potential as the junction between the lead 3 and the lead 11, and the signal corner O.sub.2 is located at the junction between the resistor 5 and the resistor 6 or a point at the same potential as the junction between the resistor 5 and the resistor 6.
If it is also assumed, according to the two-gage common-dummy method, that the leads 2, 3 and 11, 12 have negligibly small resistances r.sub.a1, r.sub.a2, r.sub.d1, r.sub.d2, and R.sub.0 =Rd=R.sub.3 =R.sub.4 as described above, then the above equation (8) is satisfied as with the one-gage two-wire method. If V=2 (V) and K=2, then the above equation (9) is satisfied. Therefore, strain .epsilon. developed in the object and stress to which the object is subjected can be calculated according to the equation (8) or (9).
According to the two-gage common-dummy method, even when the resistance of the strain gage 1 varies due to a change in the ambient temperature, the resistance of the dummy gage 10 also varies in the same manner as the resistance of the strain gage 1, and even when the resistances of the leads 2, 3 of the strain gage 1 vary due to a change in the ambient temperature, the leads 11, 12 of the dummy gage 10 vary in the same manner as the resistances of the leads 2, 3. Therefore, the two-gage common-dummy method is used as effective to cancel the effect of a change in the resistances of the strain gage 1 and the resistors 2, 3, 11, 12 due to a change in the ambient temperature on the strain measurement.
The strain measuring device for measuring strain according to the one-gage methods has a resistive circuit composed of the strain gage 1 and the resistors 4, 5, 6 of the bridges 7, 9, which are interconnected by circuit patterns on a circuit board. The strain measuring device for measuring strain according to the two-gage common-dummy method has a resistive circuit composed of the strain gages 1, 10 and the resistors 5, 6 of the bridge 13, which are also interconnected by circuit patterns on a circuit board. The strain gage 1 and the dummy gage 10 are connected to the resistive circuits by the leads, making up the bridges 7, 9, 13.
For measuring strain at a plurality of locations on an object or for measuring strain on a plurality of objects with a multispot strain measuring device, strain gages 1 (or strain gages 1 and dummy gages 10 according to the two-gage common dummy method) disposed at respective measuring spots are connected to a switch box which houses the resistive circuit. In operation, the strain gages 1 connected to the resistive circuit are successively switched by a switch in the switch box to establish the bridges 7, 9, 13 at each of the measuring spots.
In the strain measuring devices with the bridges 7, 9, 13, the power supply voltage V from the power supply is applied to the bridges 7, 9, 13, and the output voltage e of the bridges 7, 9, 13 is detected through an amplifier, an A/D converter, etc. From the data of the detected output voltage e, data indicative of strain is generated according to the equation (8) or (9). The generated strain data is then displayed on a display unit. The data of the detected output voltage e may be transmitted on-line to a personal computer or transmitted to a personal computer by a floppy disk or another recording medium. The personal computer may then generate strain data from the received data, and analyze the received data.
According to the above conventional strain measuring methods, strain is measured from the output voltage e of the bridges 7, 9, 13 according to the equation (8). Therefore, the premise of the strain measuring methods is that the output voltage e of the bridges 7, 9, 13 is e=0 when the strain gage 1 applied to the object does not develop strain, i.e., .epsilon.=0. Stated otherwise, the premise of the strain measuring methods is that the bridges 7, 9, 13 are in a state of balance when there is no resistance change depending on strain of the strain gage 1.
According to the above various strain measuring methods or the strain measuring devices based thereon, therefore, the strain gage 1, the resistors 4, 5, 6, and the dummy gage 10 are selected to have highly accurate resistances to meet the relationship R.sub.0 =R.sub.2 =R.sub.3 =R.sub.4 (the one-gage methods) or the relationship R.sub.0 =R.sub.d =R.sub.3 =R.sub.4 (the two-gage common-dummy method) for thereby equalizing the resistances of the arms of the bridges 7, 9, 13 as much as possible.
Actually, however, it is difficult to eliminate or sufficiently reduce the output voltage e of the bridges 7, 9, 13 when no strain is developed on the strain gage 1 applied to the object, because of the resistances of leads by which the strain gage 1, the resistors 4, 5, 6, and the strain gage 10 are interconnected.
Particularly, when strain is measured at a plurality of spots on a large object such as a structure or the like with the multispot strain measuring device, the leads 2, 3 or 11, 12 connecting the strain gage 1 and the dummy gage 10 to the bridges 7, 9, 13 are necessarily long and have relatively large resistances. In addition, those leads 2, 3 or 11, 12 have different lengths and hence have different resistances. As a result, in such a multispot strain measuring application, the output voltage e of the bridges 7, 9, 13 at the time no strain is developed on the strain gage 1 applied to the object may be neither eliminated nor sufficiently reduced, but may be often relatively large.
According to the above strain measuring methods, therefore, the bridges 7, 9, 13 generally produce a certain output voltage e (e.noteq.0) when no strain is developed on the strain gage 1. The output voltage e thus generated by the bridges 7, 9, 13 at the time no strain is developed on the strain gage 1 is referred to as an "initial unbalanced output voltage e.sub.0 ") Any strain .epsilon. calculated according to the equation (8) from the output voltage e generated by the bridges 7, 9, 13 which generate such initial unbalanced output voltage e.sub.0 is not accurate because even when no strain is developed on the strain gage 1, a strain .epsilon. expressed by .epsilon.=(4/K).multidot.[e.sub.0 (V-2.multidot.e.sub.0)] is calculated according to the equation (8) from the output voltage e generated by the bridges 7, 9, 13 which generate the initial unbalanced output voltage e.sub.0.
It has been customary to cancel the effect of the initial unbalanced output voltage e.sub.0 generated by the bridges 7, 9, 13 on the strain measurement as follows:
The initial unbalanced output voltage e.sub.0 generated by the bridges 7, 9, 13 is measured in advance, and an apparent strain .epsilon..sub.0 (=(4/K).multidot.[e.sub.0 /(V-2.multidot.e.sub.0)]) of the strain gage 1 which corresponds to the initial unbalanced output voltage e.sub.0 is calculated from the initial unbalanced output voltage e.sub.0 according to the equation (8) Then, the apparent strain .epsilon..sub.0 is subtracted from the strain .epsilon. which is calculated according to the equation (8) from the output voltage e generated by the bridges 7, 9, 13 upon strain measurement, thereby determining a strain .epsilon..sub.p. Stated otherwise, a strain .epsilon..sub.p is calculated from the initial unbalanced output voltage e.sub.0 and the output voltage e generated by the bridges 7, 9, 13 upon strain measurement according to the following equation (10): ##EQU3##
Since V=2 (V) and K=2, the equation (10) is rewritten as the following equation (11): ##EQU4##
However, a study conducted by the inventors of the present invention has revealed that the above process of canceling the effect of the initial unbalanced output voltage e.sub.0 on the strain measurement fails to measure strain .epsilon. (or stress depending thereon) accurately.
Specifically, as can be seen from the equation (8), the correlation between the output voltage e of the bridges 7, 9, 13 and the strain .epsilon. at the time the initial unbalanced output voltage e.sub.0 is e.sub.0 =0 is nonlinear (it may be regarded as linear insofar as the strain .epsilon. is sufficiently small), and is represented by a solid-line curve a in FIG. 4 of the accompanying drawings. The actual correlation between the output voltage e of the bridges 7, 9, 13 which is caused by the initial unbalanced output voltage e.sub.0 (e.sub.0 .noteq.0) and the strain 6 is represented by a solid-line curve b in FIG. 4. The curve b is slightly different in shape from the curve a.
According to the above process of canceling the effect of the initial unbalanced output voltage e.sub.0 on the strain measurement, as can be understood from the equation (10), the difference .epsilon..sub.p between the apparent strain .epsilon..sub.0 corresponding to the initial unbalanced output voltage e.sub.0 and a strain .epsilon..sub.xp corresponding to the output voltage e (indicated by e.sub.x in FIG. 4) obtained upon strain measurement .epsilon..sub.p (=.epsilon..sub.xp -.epsilon..sub.0) according to the solid-line curve a is determined as strain .epsilon. (=.epsilon..sub.p) free of the effect of the initial unbalanced output voltage e.sub.0.
However, the actual correlation between the output voltage e at the time initial unbalanced output voltage e.sub.0 is e.sub.0 .noteq.0 and the strain .epsilon. is represented by the solid-line curve b. Therefore, the actual strain .epsilon. corresponding to the output voltage e.sub.x upon strain measurement has a value .epsilon..sub.x in FIG. 4. Since the correlation between the output voltage e and the strain .epsilon. is nonlinear, the strain .epsilon..sub.p =.epsilon..sub.xp -.epsilon..sub.0 determined according to the conventional process and the actual strain .epsilon.=.epsilon..sub.x do not agree with each other, as can clearly be seen from FIG. 4.
Therefore, the conventional process of measuring strain while canceling the effect of the initial unbalanced output voltage e.sub.0 according to the equation (10) cannot make highly accurate strain measurement.
According to the above various strain measuring methods or the strain measuring devices based thereon, as described above, strain is basically measured according to the equation (8), and the strain gage 1, the resistors 4, 5, 6, and the dummy gage 10 are selected to have highly accurate resistances to equalize the resistances of the arms of the bridges 7, 9, 13 as much as possible. Therefore, the strain gage 1, the resistors 4, 5, 6, and the dummy gage 10 are highly expensive, and need to be fabricated according to highly advanced fabrication technology.
The strain measuring devices based on the strain measuring methods are required to take necessary measures to cancel the resistance of the circuit pattern of the resistive circuit composed of the bridges 7, 9, 13 with the strain gage 1 connected thereto, and also to employ a switch having small contact resistances for switching strain gages 1 connected to the resistive circuit for multi-spot strain measurement. As a result, the strain measuring devices are relatively expensive to manufacture.